Brian K. Kendrick

Metastable states of ozone calculated on an accurate potential energy surface

A new potential energy surface for ozone is developed. It is based on high level ab initio data and includes an accurate description of the barrier region. Full quantum reactive scattering calculations using a coupled channel approach and hyperspherical coordinates are performed on this surface for various isotopic compositions of ozone. Collision lifetimes are obtained over a wide energy range, which gives the spectrum of rovibrational metastable states (scattering resonances). This spectrum is discovered to be very nonstatistical. The spectrum of resonances is dense below the isotopic zero-point-energy threshold and sparse above it. This feature is explained by the opening of additional dissociation channels at higher energies. This behavior is a general quantum mechanical effect that should occur in other triatomic molecules.

Formation of ozone: Metastable states and anomalous isotope effect

A clear explanation for an anomalous isotope effect in ozone formation is given in terms of the energy transfer mechanism, where the metastable states of ozone are formed first, and then stabilized by collisions with other atoms. Unusual nonstatistical properties of metastable states spectra discovered earlier [J. Chem. Phys. 118, 6298 (2003)] are incorporated into the kinetics model, where different metastable states are treated as different species, and the stabilization step is treated approximately. The population of the ozone metastable states builds up and decays through three possible O2+O channels. When different isotopes of oxygen are involved the three channels become open at different energies because of the differences in the quantum zero-point-energies (ΔZPE) of the different O2 molecules. The spectrum of metastable states is anomalously dense below the ΔZPE threshold and these states are accessible only from the lower entrance channel. Also, these low-lying metastable states are stabilized v...

Potential energy surfaces for the low‐lying 2A‘ and 2A’ States of HO2: Use of the diatomics in molecules model to fit ab initio data

A DIM (diatomics in molecules) model utilizing a large basis set (34 2A‘ and 32 2A’ states) was used to obtain the potential energy surfaces relevant to the chemical reaction H+O2→OH+O. The ground state, 12A‘, surface was fitted to 910 accurate ab initio points of Walch et al. [J. Chem. Phys. 94, 7068 (1991)]. The resulting fit accurately describes the C2v conical intersection in the regions for which ab initio data are available, and the linear conical intersection is accurately described in the H+O2 region. It is also an accurate global fit with an rms deviation of 0.096 eV (2.22 kcal/mol). The behavior of the low‐lying excited states, 12A’, 22A‘, and 22A’, appears to be qualitatively correct everywhere and quantitative near the low‐lying conical intersections. The DIM formulation allows the computation of the gauge potential relevant for the description of the geometric phase and non‐adiabatic effects in multi‐surface reactive scattering calculations.

Geometric phase effects in H+O2 scattering. I. Surface function solutions in the presence of a conical intersection

The general vector potential (gauge theory) approach for including geometric phase effects in accurate 3D quantum scattering calculations in hyperspherical coordinates is presented. A hybrid numerical technique utilizing both the DVR (discrete variable representation) and the FBR (finite basis representation) is developed. This method overcomes the singular behavior of the vector potential terms giving accurate surface function solutions to the complex Hermitian nuclear Schrodinger equation. The hybrid DVR/FBR technique is applied explicitly to HO2 for zero total angular momentum. The resulting complex surface functions include the geometric phase effects due to the C2v conical intersection. The O2 permutation symmetry is implemented to give real double‐valued surface functions which exhibit both even and odd symmetry. The surface function eigenvalues are compared to calculations without the geometric phase. The results indicate that geometric phase effects should be significant for H+O2 scattering even a...

A new method for solving the quantum hydrodynamic equations of motion

The quantum hydrodynamic equations associated with the de Broglie–Bohm formulation of quantum mechanics are solved using a meshless method based on a moving least squares approach. An arbitrary Lagrangian–Eulerian frame of reference is used which significantly improves the accuracy and stability of the method when compared to an approach based on a purely Lagrangian frame of reference. A regridding algorithm is implemented which adds and deletes points when necessary in order to maintain accurate and stable calculations. It is shown that unitarity in the time evolution of the quantum wave packet is significantly improved by propagating using averaged fields. As nodes in the reflected wave packet start to form, the quantum potential and force become very large and numerical instabilities occur. By introducing artificial viscosity into the equations of motion, these instabilities can be avoided and the stable propagation of the wave packet for very long times becomes possible. Results are presented for the ...

Geometric phase effects in H+O2 scattering. II. Recombination resonances and state‐to‐state transition probabilities at thermal energies

The general vector potential (gauge theory) approach for including geometric phase effects in accurate 3D quantum scattering calculations in hyperspherical coordinates is applied to low‐energy (thermal) H+O2 collisions. The hybrid DVR/FBR (discrete variable representation/finite basis representation) numerical technique is used to obtain accurate surface function solutions which include geometric phase effects due to the C2v conical intersection in HO2. The relevant potential coupling and overlap matrices are constructed and a log‐derivative matrix of solutions to the coupled‐channel radial equations is propagated and transformed to obtain the scattering matrix S. The results for zero total angular momentum (J=0) show significant shifts in the resonance energies and lifetimes. Significant changes in the state‐to‐state transition probabilities are also observed. The results indicate that geometric phase effects must be included for H+O2 scattering even at low energies.

Cyclic-N3. II. Significant geometric phase effects in the vibrational spectra.

An accurate theoretical prediction of the vibrational spectra for a pure nitrogen ring (cyclic-N(3)) molecule is obtained up to the energy of the (2)A(2)/(2)B(1) conical intersection. A coupled-channel approach using the hyperspherical coordinates and the recently published ab initio potential energy surface [D. Babikov, P. Zhang, and K. Morokuma, J. Chem. Phys. 121, 6743 (2004)] is employed. Two independent sets of calculations are reported: In the first set, the standard Born-Oppenheimer approximation is used and the geometric phase effects are totally neglected. In the second set, the generalized Born-Oppenhimer approximation is used and the geometric phase effects due to the D(3h) conical intersection are accurately treated. All vibrational states are analyzed and assigned in terms of the normal vibration mode quantum numbers. The magnitude of the geometric phase effect is determined for each state. One important finding is an unusually large magnitude of the geometric phase effects in the cyclic-N(3): it is approximately 100 cm(-1) for the low-lying vibrational states and exceeds 600 cm(-1) for several upper states. On average, this is almost two orders of magnitude larger than in the previously reported studies. This unique example suggests a favorable path to experimental validation.

Geometric phase effects in the H+D2→HD+D reaction

The general vector potential (gauge theory) approach for including geometric phase effects in accurate three-dimensional quantum scattering calculations in symmetrized hyperspherical coordinates is applied to the H+D2(v,j)→HD(v′,j′)+D reaction at 126 values of total energy in the range 0.4–2.4 eV. State-to-state reaction probabilities, integral, and differential cross sections are computed using both the Boothroyd–Keogh–Martin–Peterson (BKMP2) and the Liu–Siegbahn–Truhlar–Horowitz potential energy surfaces for the first six values of total angular momentum (J⩽5). Calculations are performed on each surface both with and without the geometric phase. Due to symmetry, the effects of the geometric phase are shown to cancel out when contributions from even and odd values of J are added together for both the integral and differential cross sections, at all energies, and independent of which surface is used. These results are consistent with recent experimental results which are in good agreement with theoretical...

Geometric phase effects in the resonance spectrum, state-to-state transition probabilities and bound state spectrum of HO2

The general vector potential (gauge theory) approach for including geometric phase effects in accurate 3D quantum scattering calculations in hyperspherical coordinates is applied to low-energy H+O2 collisions using our new more accurate DIM (Diatomics In Molecules) potential energy surface. The newly developed hybrid DVR/FBR (Discrete Variable Representation/Finite Basis Representation) numerical technique is used to include geometric phase effects due to the C2v conical intersection in HO2. The scattering results for zero total angular momentum (J=0) computed both with and without the geometric phase show significant differences in the resonance energies and lifetimes. Significant differences in the state-to-state transition probabilities are also observed. The results indicate that geometric phase effects must be included for H+O2 scattering even at low energies. All 249 vibrational energies of HO2(2A′′) (J=0) are computed both with and without the geometric phase. Due to the localized nature of the bound state wavefunctions, no geometric phase effects are observed in the vibrational energies even in the high-lying states near dissociation.The general vector potential (gauge theory) approach for including geometric phase effects in accurate 3D quantum scattering calculations in hyperspherical coordinates is applied to low-energy H+O2 collisions using our new more accurate DIM (Diatomics In Molecules) potential energy surface. The newly developed hybrid DVR/FBR (Discrete Variable Representation/Finite Basis Representation) numerical technique is used to include geometric phase effects due to the C2v conical intersection in HO2. The scattering results for zero total angular momentum (J=0) computed both with and without the geometric phase show significant differences in the resonance energies and lifetimes. Significant differences in the state-to-state transition probabilities are also observed. The results indicate that geometric phase effects must be included for H+O2 scattering even at low energies. All 249 vibrational energies of HO2(2A′′) (J=0) are computed both with and without the geometric phase. Due to the localized nature of the bou...

Properties of nonadiabatic couplings and the generalized Born–Oppenheimer approximation

Abstract We present a new analysis of the nonadiabatic coupling terms in the coupled equations for nuclear motion wave functions when the Born–Oppenheimer (BO) representation is used for the electronic wave function. The new analysis leads to a criterion for truncating the series and neglecting terms in the coupled equations of motion. We show that in general the nonremovable part of the coupling is of the same magnitude as the removable part, except near intersections of the adiabatic states.